The Elements of Algebra |
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... rules have been fully explained , and in general rigorously proved ; so that the learner may not only become expert in the use of symbols , but also may be enabled to give a reason for each step of the investigations he pursues . In a ...
... rules have been fully explained , and in general rigorously proved ; so that the learner may not only become expert in the use of symbols , but also may be enabled to give a reason for each step of the investigations he pursues . In a ...
Page 5
... rules by which all questions of the same kind may be solved ; i.e. S D it arrives at a general answer , such as + which will suit 2 2 , every question , whatever numbers consistent with the question we put for S and D. Another , and it ...
... rules by which all questions of the same kind may be solved ; i.e. S D it arrives at a general answer , such as + which will suit 2 2 , every question , whatever numbers consistent with the question we put for S and D. Another , and it ...
Page 10
... rule : " Change the signs of all the terms of the quantity to be subtracted , or of the lower line , and then proceed as in ad- dition . " Thus , * The following proof may also be given : - Since a ab + c + b - c , for b + b = 0 and c ...
... rule : " Change the signs of all the terms of the quantity to be subtracted , or of the lower line , and then proceed as in ad- dition . " Thus , * The following proof may also be given : - Since a ab + c + b - c , for b + b = 0 and c ...
Page 14
... rules for the multi- plication and division of algebraic quantities , it will be ne- cessary that the beginner should have clear views of the nature of the positive and negative sign ; his earnest atten- tion to the next article , which ...
... rules for the multi- plication and division of algebraic quantities , it will be ne- cessary that the beginner should have clear views of the nature of the positive and negative sign ; his earnest atten- tion to the next article , which ...
Page 15
... rules only ; their general relative signification being opposition . What- ever quality or affection is expressed by + a , the contrary is expressed by a . Thus if + a represent property , -α would represent debt , if a be the length of ...
... rules only ; their general relative signification being opposition . What- ever quality or affection is expressed by + a , the contrary is expressed by a . Thus if + a represent property , -α would represent debt , if a be the length of ...
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Common terms and phrases
2ab+b² a²+2ab+b² a²x² a³b ab² ab³ algebraical quantities arithmetic mean arithmetic series arithmetical progression ax² binomial coefficient common difference compound cube root decimal denominator digits divided dividend division divisor equal examples expressed Extract the square factor Find the greatest find the numbers Find the sum fraction geometrical progression greatest common divisor greatest common measure Hence last term least common multiple less letters logarithm multiplied negative number of terms numbers in arithmetical P₁ permutations QUADRATIC EQUATIONS quotient ratio remainder result rule shew square root subtract surd third unity unknown quantity whence write written xy³
Popular passages
Page 38 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 199 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 22 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 173 - If the product of two quantities be equal to the product of two others, two of them may be made the extremes and the other two the means of a proportion.